We first must calculate how many ways 2 oblects can be chosen from 5.
combinations = 5! / 2! * (5-2)!
combinations = 5*4 / 2
combinations = 10
There are 10 ways to choose the 2 buttons and 5 ways to choose the final butto so there are 10 * 5 = 50 different ways.
Source
1728.com/combinat.htm
For this case we have a function of the form:

Where,
A: initial amount
b: growth rate (for b> 1)
x: independent variable
y: dependent variable
We then have the following function:

Using the definition, the following statements are correct:
1) The function is exponential
2) The function increases by a factor of 2.5 for each unit increase in x
3) The domain of the function is all real numbers
Answer:
Hello your question is incomplete attached below is the complete question
Ix = 0 Ux = 
Iz = 0 Uz = 
Iy = 5 Uy = 10
Step-by-step explanation:
Ix = 0 Ux = 
Iz = 0 Uz = 
Iy = 5 Uy = 10
attached below is the detailed solution
Answer:
a.) C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH b.) $170
Step-by-step explanation:
(a) Marginal cost is defined as the decrease or increase in total production cost if output is increased by one more unit. Mathematically:
Marginal cost (MC) = change in total cost/change in quantity
Therefore, to derive the equation for total production cost, we need to integrate the equation of marginal cost with respect to quantity. Thus:
Total cost (C) = Integral [3(q-4)^2] dq = -(1/4)*(q-4)^3 + k
where k is a constant.
The overhead (OH) = C(0) = -(1/4)*(0-4)^3 + k = -16 + k
C(q) = -(1/4)*(q^3 - 12q^2 + 48q - 64) + k = -(1/4)*q^3 + 3q^2 - 12q -16 + k
Thus:
C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH
(b) C(14) = -(1/4)*14^3 + 3*14^2 - 12*14 + 436 = -686 + 588 - 168 + 436 = $170